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We propose a new recursive estimator for linear dynamical systems under Gaussian process noise and non-Gaussian measurement noise. Specifically, we develop an approximate maximum a posteriori (MAP) estimator using dynamic programming and…
We demonstrate optimal state estimation for a cavity optomechanical system through Kalman filtering. By taking into account nontrivial experimental noise sources, such as colored laser noise and spurious mechanical modes, we implement a…
Measuring the effect of gravity on antimatter is a longstanding problem in physics that has significant implications for our understanding of the fundamental nature of the universe. Here, we present a technique to measure the gravitational…
An analytical expression for the gravitational field of a homogeneous cylinder is derived. The phase of the atom interferometer produced by the gravity field of the set of cylinders has been calculated. The optimal values of the initial…
Noise properties of an idealized atomic magnetometer that utilizes spin squeezing induced by a continuous quantum nondemolition measurement are considered. Such a magnetometer measures spin precession of $N$ atomic spins by detecting…
Detections of gravitational waves (GW) in the frequency band 35 Hz to 500 Hz have led to the birth of GW astronomy. Expected signals above 500 Hz, such as the quasinormal modes of lower mass black holes and neutron star mergers signatures…
In the detection of gravitational waves in space, during the science phase of the mission, the point ahead angle mechanism (PAAM) serves to steer a laser beam to compensate for the angle generated by the relative motion of the two…
The circadian clock is an internal timer that coordinates the daily rhythms of behavior and physiology, including sleep and hormone secretion. Accurately tracking the state of the circadian clock, or circadian phase, holds immense potential…
It is shown in the present Letter that the quantum noise due to high laser intensities in Michelson interferometer for gravitational waves detection can be reduced by sending squeezed vacuum states to the 'dark' port of the interferometer.…
The filtering distribution captures the statistics of the state of a dynamical system from partial and noisy observations. Classical particle filters provably approximate this distribution in quite general settings; however they behave…
Position-meter and speed-meter interferometers have been analysed for detecting gravitational waves. We introduce the concept of acceleration measurement in comparison with position and speed measurement. In this paper, we describe a…
The analysis of high-dimensional dynamical systems generally requires the integration of simulation data with experimental measurements. Experimental data often has substantial amounts of measurement noise that compromises the ability to…
Geometry of the state space is known to play a crucial role in many applications of Kalman filters, especially robotics and motion tracking. The Lie group-centric approach is currently very common, although a Riemannian approach has also…
We consider the problem of state estimation in dynamical systems and propose a different mechanism for handling unmodeled system uncertainties. Instead of injecting random process noise, we assign different weights to measurements so that…
This paper describes a novel method for the estimation of the trajectory curve and orientation of a rigid body moving along a railway track. Compared to other recent developments in the literature, the presented approach has the significant…
We present a numerical method, based on a FEM simulation, for the determination of the gravitational field generated by massive objects, whatever geometry and space mass density they have. The method was applied for the determination of the…
This work introduces an algorithm for state estimation on manifolds within the framework of the Kalman filter. Its primary objective is to provide a methodology enabling the evaluation of the precision of existing Kalman filter variants…
We propose a quantum imaging-inspired setup for measuring gravitational fields using an atom that emits a photon at one of two possible locations. The atom acquires a gravitationally induced quantum phase that it shares with the photon. By…
Filtering and smoothing algorithms for linear discrete-time state-space models with skewed and heavy-tailed measurement noise are presented. The algorithms use a variational Bayes approximation of the posterior distribution of models that…
Estimating the statistics of the state of a dynamical system, from partial and noisy observations, is both mathematically challenging and finds wide application. Furthermore, the applications are of great societal importance, including…